Question

the function f(x)=3x^3+x^2+2x rises as x grows very small

Answer 1

True or False??

Answer 2

thats false

Answer 3

because very small means closer to 0. as x approaches 0, f(x) approaches 0 as well. you can see this by simply plugging in 0 for x and getting f(x) = 0.

Answer 4

there are other ways to solve this as well. the method described above is taking the limit of f(x) as x approaches 0. you can also differentiate the function and see that it is monotonic (its slope is always positive or negative) from x = 0 to x = ∞, which implies that f(x) rises as x gets very big. graphing the function also allows you to see that f(x) gets smaller as x approaches 0